Lattice Boltzmann method for compressible Euler equations based on exact kinetic system,International Journal for Numerical Methods in Fluids

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Lattice Boltzmann method for compressible Euler equations based on exact kinetic system
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-04-04 , DOI: 10.1002/fld.4987
Takaya Hanada ₁ , Takeshi Kataoka ₁

Affiliation

We have developed a new type of simple lattice Boltzmann (LB) model for the compressible Euler equations based on the collisionless kinetic-equation approach proposed by Sone. The model uses the collisionless kinetic equation in the streaming process, and modifies the distribution function to its Chapmanâ€“Enskog type at each time step. Compared with the current LB models which solve the kinetic equation of the BGK type, the proposed model is superior in the following two points: (i) Inviscid flows can be computed stably while there is no such model in the current LBM; (ii) The velocity distribution function does not need to be memorized in computation. We calculate various inviscid compressible flows described by the compressible Euler equations using our new one-, two-, and three-dimensional models. Numerical results show the capability of our scheme to simulate high-speed supersonic flows with shock waves.

中文翻译：

基于精确动力学系统的可压缩欧拉方程的格子Boltzmann方法

我们基于 Sone 提出的无碰撞动力学方程方法，为可压缩欧拉方程开发了一种新型的简单格子 Boltzmann (LB) 模型。该模型在流过程中使用无碰撞动力学方程，并在每个时间步将分布函数修改为其 Chapman-Enskog 类型。与目前求解BGK型动力学方程的LB模型相比，该模型在以下两点具有优越性：(i)在目前LBM中没有这种模型的情况下，可以稳定地计算无粘流；(ii) 速度分布函数在计算中不需要记忆。我们使用新的一维、二维和三维模型计算由可压缩欧拉方程描述的各种无粘性可压缩流动。

更新日期：2021-04-04

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